Mohammed-Baqer Qalibaf, mayor of Tehran, likes to be hands-on. On a recent morning, he strode into the citizens' complaint center he set up at city hall and took some calls. Qalibaf handled a bureaucratic delay in the issuing of a building permit, displaying the commitment to accountability that has many of the capital's residents praising him. "We had the worst snow this year, and Qalibaf had it cleared in one day," says Mohsen Rejai, a company clerk. "That's the kind of mayor we need."

Being mayor of Tehran may not be the summit of Qalibaf's political ambitions. Iran...